Mix Shader between values of 0 - 0.5 is the same as 0
It sounds like you probably have your material’s Blend Mode set to Alpha Clip:

The Alpha Clip blend mode is controlled by the Clip Threshold setting, which defaults to 0.5. This means that wherever your material’s opacity is below 0.5, it will render as fully transparent, and wherever it’s above 0.5, it will render as fully opaque. This clearly isn’t what you want.
Instead, you should change the Blend Mode setting to Alpha Blend. This will blend your object against objects behind it, giving you the smooth transition you’re looking for. You may also wish to disable the Show Backface option to ensure the whole mesh has a uniform transparency.